Question

The rate consnt for a reaction is measured as a function of temperature. A plot of ln k versus 1/T is linear and has s slope of -1.01 x 1-^4K. Calculate the activation energy for the reaction

Answer 1

Answer : The activation energy for the reaction is, $8.39\times 10^4J$

Explanation :

According to the Arrhenius equation,

$K=A\times e^{\frac{-Ea}{RT}}$

Taking logarithm on both side, we get:

$\ln K=\frac{-Ea}{RT}+\ln A$

where,

$Ea$ = activation energy for the reaction

R = gas constant = 8.314 J/mole.K

T = temperature

K = rate constant

A = pre-exponential factor

The linear equation expression is:

y = mx + c

Plot of ln (K) versus (1/T) gives a straight line with a slope is equal to, $\frac{-Ea}{R}$

As we are given that:

Slope = $-1.01\times 10^4K$

So,

$Slope=\frac{-Ea}{R}=-1.01\times 10^4K$

$-Ea=-1.01\times 10^4K\times R$

$Ea=1.01\times 10^4K\times 8.314J/mol.K$

$Ea=83971.4J=8.39\times 10^4J$

Thus, the activation energy for the reaction is, $8.39\times 10^4J$